Context. Low-mass protostars drive powerful molecular outflows that can be observed with mm and sub-mm telescopes. Various sulfuretted species are known to be bright in shocks and could be used to infer the physical and chemical conditions throughout the observed outflows. Aims. The evolution of sulfur chemistry is studied along the outflows driven by the NGC1333-IRAS4A protobinary system located in the Perseus cloud to constrain the physical and chemical processes at work in shocks. Methods. We observed various transitions from OCS, CS, SO, and SO$_2$ towards NGC1333-IRAS4A in the 1.3, 2, and 3mm bands using the IRAM NOEMA array and we interpreted the observations through the use of the Paris-Durham shock model. Results. The targeted species clearly show different spatial emission along the two outflows driven by IRAS4A. OCS is brighter on small and large scales along the south outflow driven by IRAS4A1, whereas SO$_2$ is detected rather along the outflow driven by IRAS4A2 that is extended along the north east - south west (NE-SW) direction. Column density ratio maps estimated from a rotational diagram analysis allowed us to confirm a clear gradient of the OCS/SO$_2$ column density ratio between the IRAS4A1 and IRAS4A2 outflows. SO is detected at extremely high radial velocity up to 25 km/s relative to the source velocity, clearly allowing us to distinguish the two outflows on small scales. Conclusions. The observed chemical differentiation between the two outflows of the IRAS4A system could be explained by a different chemical history. The outflow driven by IRAS4A1 is likely younger and more enriched in species initially formed in interstellar ices, such as OCS, and recently sputtered into the shock gas. In contrast, the longer and likely older outflow triggered by IRAS4A2 is more enriched in species that have a gas phase origin, such as SO$_2$.
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